An Energy-optimal Relative-angle-constrained Cooperative Guidance Method Based on Distributed Convex Optimization

doi:10.12382/bgxb.2024.0739

Abstract

Abstract:

The angle-optimal cooperative guidance of multiple aerial vehicles enables multi-directional interception of maneuvering targets with minimal energy consumption,which is an important research direction in the field of guidance.The current optimal cooperative guidance methods depend on global information and centralized communication which has low reliability in practical applications.To address the issue mentioned above,an energy-optimal relative-angle-constrained cooperative guidance method based on distributed convex optimization is proposed to resolve the contradiction between the locality of distributed information and the global optimality of cooperative commands.Based on the generalized trajectory shaping guidance law (GTSG),the mapping relationship between aerial vehicle control energy and desired terminal line-of-sight (LOS) angle is derived.A convex objective function is formulated using total control energy,and the convex constraints are established based on relative LOS angle constraints,thereby constructing a distributed convex optimization problem.The extended primal-dual algorithm (EPDA) is then introduced to achieve distributed global optimization,enabling the real-time coordination of aerial vehicle LOS angles for minimum-energy interception.The simulated results and analysis demonstrate that the proposed method does not rely on a central node while ensuring global energy optimality compared with existing centralized angle-coordinated guidance algorithms.

Key words: cooperative guidance, relative LOS angle constraint, energy-optimal, distributed convex optimization, primal-dual algorithm, maneuvering target

WANG Jiang, ZHU Ziyang, LI Hongyan, WANG Peng. An Energy-optimal Relative-angle-constrained Cooperative Guidance Method Based on Distributed Convex Optimization[J]. Acta Armamentarii, 2025, 46(6): 240739-.

Figures/Tables 20

Fig.1 Geometric relationship between multiple aerial vehicles and target

Fig.2 Aerial vehicle-target model for linearization

Fig.3 Block diagram of the working principle of the proposed guidance method

Table 1 Initial simulation conditions

飞行器	位置/m	速度/(m·s^-1)	航迹角/deg
M₁	(0,0)	800	0
M₂	(0,0)	800	5
M₃	(0,0)	800	10
M₄	(0,0)	800	15
T	(0,0)	500	180

Fig.4 Communication topology for 4 aerial vehicles

Fig.5 Simulated results of the proposed guidance method

Fig.6 Simulated results of the cooperative guidance method in Ref.[5]

Table 2 Terminal LOS angles of aerial vehicles

采用制导律	终端视线角/deg
本文制导律	[19.45,9.45,-1.45,-11.45]
文献[5]制导律	[12.72,2.72,-7.28,-17.28]

Table 3 Energy consumption of aerial vehicles

采用制导律	总能量消耗/(m²·s^-3)
本文制导律	6.42×10⁴
文献[5]制导律	1.70×10⁵

Table 4 Intervals of variables

初始仿真条件	正态分布
飞行器速度V_M/(m·s^-1)	N(800,20²)
飞行器初始航迹角γ₀/deg	N(10,5²)
目标速度V_T/(m·s^-1)	N(600,20²)
目标初始航迹角 $γ T 0$ /deg	N(150,10²)
目标初始横坐标 $x T 0$ /m	N(6000,100²)
目标初始纵坐标 $y T 0$ /m	N(0,100²)
目标加速度 $a M i$ /(m·s^-2)	N(-49.1,4.91²)

Table 4 Intervals of variables

初始仿真条件	正态分布
飞行器速度V_M/(m·s^-1)	N(800,20²)
飞行器初始航迹角γ₀/deg	N(10,5²)
目标速度V_T/(m·s^-1)	N(600,20²)
目标初始航迹角 $γ T 0$ /deg	N(150,10²)
目标初始横坐标 $x T 0$ /m	N(6000,100²)
目标初始纵坐标 $y T 0$ /m	N(0,100²)
目标加速度 $a M i$ /(m·s^-2)	N(-49.1,4.91²)

Fig.7 Monte Carlo simulation results

Table 5 The mean values of various performance indicators

采用制导律	总能量消耗/ (m²·s^-3)	脱靶量/m	视线角误差/deg
本文制导律	4.33×10⁴	0.5196	0.4396
文献[5]制导律	2.26×10⁵	0.5245

Fig.8 Communication topology for 4 aerial vehicles

Fig.9 Dynamic variation law of distributed topology

Fig.10 Simulated results of dynamic topology variation

Table 6 Comparison of simulated results

拓扑是否变化	终端视线角/deg	总能量消耗/(m²·s^-3)
是	[19.45,9.45,-1.45,-11.45]	6.42×10⁴
否	[19.45,9.45,-1.45,-11.45]	6.42×10⁴

Table 7 The initial simulation conditions

飞行器	位置/m	速度/(m·s^-1)	航迹角/deg
M₁	(0,3000)	800	0
M₂	(0,3000)	800	5
M₃	(0,3000)	800	10
M₄	(0,3000)	800	15
T	(6000,3000)	500	180

Table 8 Aerodynamic coefficients and derivatives

马赫数	$C l a l$ /(rad^-1)	C_d0	$C d a l 2$ /(rad^-2)
1.5	27.47	0.575	38.48
2.0	23.83	0.443	30.15
2.5	21.28	0.383	26.12
3.0	19.54	0.352	24.07

Table 8 Aerodynamic coefficients and derivatives

马赫数	$C l a l$ /(rad^-1)	C_d0	$C d a l 2$ /(rad^-2)
1.5	27.47	0.575	38.48
2.0	23.83	0.443	30.15
2.5	21.28	0.383	26.12
3.0	19.54	0.352	24.07

Fig.11 Simulated results of the proposed guidance method

Fig.12 Comparison of speed changes of aerial vehicles guided by the proposed method and the method in Ref.[5]

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